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Abstract:

A method of providing a polarized radio frequency scanning source is
provided. The method including amplitude modulating at least two
synchronized polarized radio frequency (RF) carrier signals with a
predetermined relationship between their amplitude modulation of their
electric field components and their polarization states to provide a
scanning polarized RF reference source with a desired scanning range,
pattern and frequency. The two or more synchronized polarized RF carrier
signals with the predetermined relationship between their amplitude
modulation can obtain a periodic or non-periodic scanning range, rate and
frequency.

Claims:

1. A method of providing a polarized radio frequency scanning source, the
method comprising amplitude modulating at least two synchronized
polarized radio frequency (RF) carrier signals with a predetermined
relationship between their amplitude modulation of their electric field
components and their polarization states to provide a scanning polarized
RF reference source with a predetermined scanning range, pattern and
frequency.

2. The method of claim 1, wherein the two or more synchronized polarized
RF carrier signals with the predetermined relationship between their
amplitude modulation obtain a periodic scanning range, rate and
frequency.

3. The method of claim 1, wherein the two or more synchronized polarized
RF carrier signals with the predetermined relationship between their
amplitude modulation obtain a non-periodic scanning range, rate and
frequency.

4. A polarized radio frequency scanning source comprising means for
amplitude modulating at least two synchronized polarized radio frequency
(RF) carrier signals with a predetermined relationship between their
amplitude modulation of their electric field components and their
polarization states to provide a scanning polarized RF reference source
with a predetermined scanning range, pattern and frequency.

Description:

CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] The present application is a continuation application of U.S.
application Ser. No. 11/888,797 filed Aug. 2, 2007 which claims priority
to U.S. provisional patent application, Ser. No. 60/835,022, filed on
Aug. 2, 2006, the entire contents of each of which is incorporated herein
by reference.

[0005] For guidance and/or steering purposes, all manned and unmanned
mobile platforms, such as land vehicles, powered or non-powered airborne
platforms, surface or submerged marine platforms, or various space
vehicles, require onboard information as to their absolute (relative to
earth) position and orientation (sometimes called attitude) or their
position and orientation relative to another object such as a reference
platform or a target object.

[0006] This position and orientation information is particularly important
for unmanned and guided platforms such as mobile robots. Unmanned Aerial
Vehicles (UAV), unmanned guided surface or submerged platforms, and the
like. This is also the case in future smart and guided projectiles,
including gun-fired munitions, mortars and missiles. Such platforms will
also require the aforementioned absolute and/or relative position and
orientation information onboard the platform for closing the feedback
guidance and control loop to guide the platform to the desired target or
track a specified trajectory or the like.

[0007] In certain cases, the onboard position and orientation information
(absolute or relative to the target, a reference station, another mobile
platform, etc.) can be provided by an outside source, for example, by GPS
for position or by a radar reading or optical signal that is reflected
off some target or received by the mobile platform. In other cases, it is
either required or is highly desirable to have autonomous sensors on
board the mobile platform, including gun-fired projectiles, mortars and
missiles, to directly measure the position and orientation of the object
with respect to a fixed object (for example a ground station) or a moving
object (for example a moving target).

[0008] It is noted that even though in this disclosure all references are
made to moving platforms, it will be appreciated by those of ordinary
skill in the art that the provided description also includes the
measurement of the position and orientation of one object relative to
another object, one or both of which may be fixed to a third object such
as the ground.

[0009] Currently available sensors for remote measurement of the angular
position (attitude) of an object relative to the earth or another object
(target or weapon platform) can be divided into the following five major
classes.

[0010] The first class of sensors measure changes in the angular position
using inertial devices such as accelerometers and gyros. Inertial based
angular orientation sensors, however, generally suffer from drift and
noise error accumulation problems. In such sensors, the drift and the
measurement errors are accumulated over time since the acceleration has
to be integrated twice to determine the angular position. As a result,
the error in the angular position measurement increases over time. In
addition, the initial angular orientation and angular velocity of the
object must be known accurately. Another shortcoming of inertia based
angular position sensors is that the angular position of one object
relative to another cannot be measured directly, i.e., the orientation of
each object relative to the inertia frame has to be measured separately
and used to determine their relative angular orientation. As a result,
errors in both measurements are included in the relative angular
orientation measurement, thereby increasing it even further. In addition,
electrical energy has to be spent during the entire time to continuously
make such sensory information.

[0011] In the particular case of gun-fired munitions, two other major
problems are encountered with inertia-based sensors. Firstly, they have
to be made to withstand firing accelerations that in certain cases could
be in excess of 100,000 Gs. However, to achieve the required guidance and
control accuracy over relatively long distances and related times, the
absolute angular orientation of the projectile has to be known during the
entire time of the flight within very small angles corresponding to
sub-fractions of one G. As a result, the accelerometer is prone to a
settling time problem, particularly with the aforementioned initial high
G loading. Obviously, the development of inertia based accelerometers and
gyros that could withstand the aforementioned high G levels and require
near zero settling time is an extremely difficult task.

[0012] The second class of angular orientation sensors operates using
optical methods. Such sensory systems can directly measure angular
position of one object relative to another. However, optical based
angular position sensory systems suffer from several disadvantages,
including operation only in the line of sight between the two objects;
accurate measurement of relative angular orientation only if the objects
are relatively close to each other; limited range of angular orientation
measurement; relatively high power requirement for operation; requirement
of relatively clean environment to operate; and in military applications
the possibility of exposing the site to the enemy and jamming. Optical
gyros do not have most of the above shortcomings but are relatively
large, require a considerable amount of power, and are difficult to
harden for high G firing accelerations. Optical methods such as tracking
of projectiles with surface mounted reflectors and the like have also
been developed, which are extremely cumbersome to use even during
verification testing, suffer from all the aforementioned shortcomings,
and are impractical for fielded munitions. In addition, the information
about the object orientation can usually be determined only at the ground
station and has to be transmitted to the moving object for guidance and
control purposes. As a result, optical angular position sensors are
generally not suitable for munitions and other similar applications.

[0013] The third class of angular orientation sensors is magnetometers
that can be used to measure orientation relative to the magnetic field of
the earth. The main problem with magnetometers is that they cannot
measure orientation of the object about the magnetic field of the earth.
Other important issues are low sensitivity; requirement of an accurate
map of the magnetic field in the area of operation; and sensitivity to
the presence of vehicles and the like in the area, the configuration of
which usually varies in time, particularly in an active war theatre.

[0014] The fourth class of angular orientation measurement systems are
based on the use of radio frequency (RF) antennas printed or placed on
the surface of an object to reflect RF energy emanating from a
ground-based radar system. The reflected energy is then used to track the
object on the way to its destination. With two moving objects, the radar
measures the time difference between the return signals from each of the
objects and thereby determines angular information in terms of the angle
that the relative velocity vector makes with respect to a coordinate
system fixed to one of the objects. With such systems, measurement of
full spatial orientation of an object (relative to the fixed radar or a
second object) is very difficult. In addition, the information about the
object orientation is determined at the radar station and has to be
transmitted back to the moving object(s) if it is to be used for course
correction. It is also very difficult and costly to develop systems that
could track multiple projectiles. It is noted that numerous variations of
the above method and devices have been devised with all suffering from
similar shortcomings.

[0015] In addition to the above angular orientation measurement sensors.
GPS signals have also been used to provide angular orientation
information. Such systems, however, have a number of significant
shortcomings, particularly for munitions applications in general and gun
fired munitions and mortars in particular. These include the fact that
GPS signals may not be available along the full path of the flight; such
orientation sensory systems are generally not very accurate; and the
measurements cannot be made fast enough to make them suitable for
guidance and control purposes in gun fired munitions and mortars. In
addition, GPS signals are generally weak and prone to jamming.

[0016] The fifth class of angular orientation sensors is based on
utilizing polarized Radio Frequency (RF) reference sources and mechanical
cavities as described in U.S. Pat. Nos. 6,724,341 and 7,193,556 and U.S.
patent application publication number 2007/0001051, all of which are
incorporated herein by reference, and hereinafter are referred to as
"polarized RF angular orientation sensors". These angular orientation
sensors use highly directional mechanical cavities that are very
sensitive to the orientation of the sensor relative to the reference
source due to the cross-polarization and due to the geometry of the
cavity. The reference source may be fixed on the ground or may be another
mobile platform (object). Being based on RF carrier signals, the sensors
provide a longer range of operation. The sensors can also work in and out
of line of sight. In addition, the sensors make angular orientation
measurements directly and would therefore not accumulate measurement
error. The sensor waveguides receive and record the electromagnetic
energy emitted by one or more polarized RF sources. The angular position
of a waveguide relative to the reference source is indicated by the
energy level that it receives. A system equipped with multiple such
waveguides can then be used to form a full spatial orientation sensor. In
addition, by providing more than one reference source, full spatial
position of the munitions can also be measured onboard the munitions.

[0017] The aforementioned polarized RF based angular orientation sensors
provide highly precise angular orientation measurements. The sensors,
when embedded in a mobile platform such as in a projectile, can measure
full angular orientation of the projectile (mobile platform) relative to
the fixed ground station or another moving object such as a UAV or
another projectile (mobile platform) where the reference source is
located. These angular orientation sensors are autonomous, i.e., they do
not acquire sensory information through communication with a ground,
airborne or the like source. The sensors are relatively small and can be
readily embedded into the structure of most mobile platforms including
munitions without affecting their structural integrity. As a result, such
sensors are inherently shock, vibration and high G acceleration hardened.
A considerable volume is thereby saved for use for other gear and added
payload. In addition, the sensors become capable of withstanding
environmental conditions such as moisture, water, heat and the like, even
the harsh environment experienced by munitions during firing. In
addition, the sensors require a minimal amount of onboard power to
operate.

[0018] The latter two classes of RF based full angular orientation and
full position sensors promise to provide low cost, small volume and
lightweight, low power, precision and autonomous onboard sensors for
guidance and control of all mobile platforms, including future smart and
precision guided munitions, as alternatives to inertia-based, optical,
GPS and other similar currently available sensors.

[0019] The latter two classes of RF based full angular orientation sensors
are dependent on the magnitude of the received signal at the sensors from
the reference source to determine the orientation of the sensor relative
to the reference source. This is the case, for example, for the
aforementioned angular orientation sensors which are based on utilizing
polarized Radio Frequency (RF) reference sources and mechanical cavities
as described in U.S. Pat. Nos. 6,724,341 and 7,193,556 and U.S. patent
application publication number 2007/0001051.

[0020] Briefly, referring now to FIGS. 1 and 2, there is shown a
representation of a waveguide sensor 100 and its operation with respect
to a polarized radio frequency (RF) reference (illuminating) source 101.
An electromagnetic wave consists of orthogonal electric (E) and magnetic
(H) fields. The electric field E and the magnetic field H of the
illuminating beam are mutually orthogonal to the direction of propagation
of the illumination beam. When polarized, the planes of E and H fields
are fixed and stay unchanged in the direction of propagation. Thus, the
illuminating source establishes a (reference) coordinate system with
known and fixed orientation. The waveguide 100 reacts in a predictable
manner to a polarized illumination beam. When three or more waveguides
are distributed over the body of an object, and when the object is
positioned at a known distance from the illuminating source, the
amplitudes of the signals received by the waveguide sensor 100 can be
used to determine the orientation of the object relative to the reference
(illuminating) source 101, i.e., in the aforementioned reference
coordinate system of the reference source 101. The requirement for the
proper distribution of the waveguide sensors 100 over the body of the
object is that at least three of the waveguides be neither parallel nor
co-planar.

[0021] It is therefore observed that the aforementioned classes of RF
based full angular orientation sensors are dependent on the magnitude of
the received signal at the sensors from the reference source to determine
the orientation of the sensor relative to the reference source. The use
of the signal magnitude, however, has several major shortcomings that
limits the utility of such sensors as well as degrades their angular
orientation measurement precision. The following are the major
shortcomings of the aforementioned use of signal magnitude information in
these sensors for measuring angular orientation relative to the polarized
RF reference source: [0022] 1. To relate the magnitude of the received
signal to angular orientation, the distance from the reference source to
the angular orientation sensors must be known. This in general means that
other means have to be also provided to measure or indicate the position
of the orientation sensor relative to the reference source. [0023] 2. In
practice, the signal received at the angular orientation sensor would be
noisy, it may face losses due to the environmental conditions, and is
also prone to measurement errors at the sensor. [0024] 3. The magnitude
of the signal received at the angular orientation sensors and its
relationship to the angular orientation of the sensors (object to which
the sensors are attached) could be significantly different when the
object is not in the line-of-sight of the reference source. Therefore
when the object is not in the line-of-sight, the use of the received
signal magnitude information could in general lease to significant
degradation of the accuracy of the angular orientation measurements.

SUMMARY OF THE INVENTION

[0025] The use of polarized RF reference sources with scanning capability
would significantly reduce or eliminate the aforementioned shortcomings
of the RF based full angular orientation sensors. This would be the case
since scanning provides the means to use various well established
techniques such as peak detection and a novel nonlinear signal processing
method based on a curve matching and scaling, which is disclosed later in
this disclosure, and thereby significantly increase the angular
orientation measurement precision, in certain cases by several orders of
magnitude; filtering out the noise and effects of reflections and
multi-paths; making it possible to use these angular orientation sensors
in both line-of-sight and non-line-of-sight settings; and also eliminates
the need to know the distance between the reference source and the
angular orientation sensors. It is also shown later in this disclosure
that the use of polarized RF reference sources with scanning capability
would have additional advantages. For example, the precision with which
the angular orientation is measured by the sensors is not dependent on
the accurate calibration of the received signal magnitude information
(usually surfaces). In addition, particularly for line-of-sight
applications, if such calibration has been made, then as discussed below,
the information can be used to calculate the distance between the
reference source to the sensors (object) as well.

[0026] In addition, when more than one polarized RF reference source is
used to measure the position of the sensors (object) in the coordinate
system fixed to the reference sources, the use of polarized RF reference
sources with scanning capability would significantly increase the
accuracy of these measurements.

[0027] A need therefore exists for polarized RF reference sources with
scanning capability. This is particularly the case since such reference
sources would allow the aforementioned RF angular orientation sensors to
be used in both line-of-sight as well as in non-line-of-sight, in
addition to making them significantly more accurate and tolerant to noise
and other environmental effects, and when calibrated would allow them to
measure distance between the reference source and the angular orientation
sensors (object) in addition to the angular orientation measurement.

[0028] An objective of the present invention is to provide a method and
system for polarized RF reference sources with scanning capability,
thereby allowing a significant increase in the angular orientation
measurement precision of the aforementioned angular orientation sensors;
filtering out the noise and effects of reflections and multi-paths;
making it possible to use these angular orientation sensors in both
line-of-sight and non-line-of-sight settings; and measure the distance
between the reference source and the angular orientation sensors
(object), particularly in line-of-sight situations. Such polarized RF
reference sources with scanning capability can be designed to provide
almost any desired scanning range and scanning frequency, ranging from Hz
to KHz or even MHz frequencies, even non-sinusoidal patterns, to fit the
application at hand.

[0029] Another objective of the present invention is to provide a novel
nonlinear signal processing method based on a curve matching and scaling
technique, thereby increasing the accuracy of the angular orientation
(and distance between the reference source and the sensors, i.e., object,
particularly in line-of-sight situations) measurement of the
aforementioned angular orientation sensors. In certain applications, the
use of non-sinusoidal scanning patterns has added advantages, some of
which are described below.

[0030] Another objective of the present invention is to provide a method
and system for establishing an angular orientation reference source for a
large area, for example the field of operation of certain mobile
platforms, such as the field of operation of mobile robotic platforms
being used for rescue operations in certain fields. Such a referencing
system may be used to serve as a full positioning as well angular
orientation system.

[0031] Yet another objective of the present invention is to provide the
method and system of establishing "homing" planes and/or lines (with or
without directional indication) and/or points. Such "homing" "signals"
can then be used by the mobile platform for guidance, e.g., for guiding
it towards or away from a point or move towards a line and then follow
certain.

[0032] It is noted that the disclosed methods and systems can allow the
scanning capability of the present polarized RF source to be achieved
without the use of any mechanical components and by the use of simple
electronic circuitry using modulated signals of various patterns. As a
result, the scanner can achieve almost any rate, any scanning pattern,
scanning frequencies ranging from zero to several Hz, or KHz, or MHz
depending on the application at hand.

[0033] In addition, the disclosed polarized RF reference sources with
scanning capability can be programmed to provide random scanning signals
with very low power levels or on-off (pulsed) signals to avoid detection
or utilize other detection avoidance procedures.

[0034] In addition, the disclosed method can readily allow the prior art
polarized RF reference sources to scan more than one range, for example
for providing a relatively narrow scanning range for more than one
angular orientation.

BRIEF DESCRIPTION OF THE DRAWINGS

[0035] These and other features, aspects, and advantages of the apparatus
of the present invention will become better understood with regard to the
following description, appended claims, and accompanying drawings where:

[0036] FIGS. 1 and 2 illustrate a schematic representation of a waveguide
sensor with respect to a polarized radio frequency (RF) reference
(illuminating) source of the prior art.

[0037]FIG. 3 illustrates a graph where mx=0, my=0.5, and
E0x=E0y, and the reference sources are positioned at the origin
of the Cartesian XY coordinate system O.

[0040] An electromagnetic wave is a propagation of electric and magnetic
field disturbances in unison such that both electric and magnetic field
vectors are perpendicular to the direction of propagation and to each
other, they are in phase and in vacuum the ratio of their magnitude is
constant. The wave is transverse (oscillations are perpendicular to the
direction of propagation) and its velocity in free space is determined by
the permittivity and permeability of free space. The polarization state
of an electromagnetic wave is defined by the oscillation state of its
transverse electric field in the plane perpendicular to propagation
direction. Since the magnetic field is always perpendicular to the
electric field and has a proportional magnitude it is redundant for the
characterization of polarization. The magnitudes and phases of orthogonal
components of electric field do not necessarily have the same values and
the periodic curve traced out by the tip of the electric field vector
describes the different states of polarization.

[0041] The electromagnetic waves in free space are described by the
Maxwell equations without the charges and currents are

where E and B are respectively the electric and magnetic (induction)
fields, and ε0 and μ0 respectively denote the
permittivity and permeability of free space. From Maxwell's equations one
derives the following linear wave equations

[0042] To specify the polarization state of electromagnetic waves we look
for the harmonic traveling plane wave solutions of the electric field
wave equation describing the waves propagating in the z-direction. In
orthogonal coordinates XYZ these solutions are given by

E(z,t)=Ei+Eyj-E0x cos(ω-kz)+E0x
cos(ω-kz-δ)j

where ω is the angular frequency, δ denotes the phase angle
difference between the x and y components of electric field. k is the
z-component of wave number vector which is related to the wavelength
λ with |k-2π/λ and parallel to the direction of
propagation. E0x and E0y are the (positive) amplitudes of x and
y components of electric field components, respectively, and i and j are
unit vectors in the x and y directions of the aforementioned Cartesian
coordinate system XYZ.

[0043] Consider a situation in which the polarization states associated
with the components Ex and Ey are given as

Ex=E0x cos(ωt-kz)

Ey=E0y cos(ωt-kz+δ)

Then the following characteristic can be defined: [0044] a) For δ :
2 πn, n 1, 2, 3, . . . , the electric field components are in phase
and their ratio Ex Ey is a positive constant, in this case we
have a so-called linearly polarized or plane polarized wave. The tip of
electric field vector traces out a line in the xy-plane which defines the
polarization direction, and

[0044] Ex=E0x cos(ωt-kz)

Ey=E0y cos(ωt-kz) [0045] b) For δ -π: 2 π n,
n 1, 2, 3, . . . , we have an out of phase linear polarization with the
component ratio equal to a negative constant, and

[0045] Ex=E0x cos(ωt-kz)

Ey=-E0y cos(ωt-kz) [0046] c) For δ π 2 : 2 π
n, n 1, 2, 3, . . . , and E0x E0y, the electric field vector
rotates in the xy-plane clockwise (as seen against propagation) without
changing its magnitude and it is in a state of right circular
polarization, and

Ey=E0 sin(ωt-kz) [0048] e) For δ -π 2=2 π n,
n -1, 2, 3, . . . and Ex0≠E0y, we have a more general
case of right elliptical polarization. Electric field components have
different amplitudes and the y-component leads with ninety degrees of
phase; the tip electric field vector rotates clockwise and traces out an
ellipse, and

[0048] Ex=E0x cos(ωt-kz)

Ey=-E0y sin(ωt-kz)

f) For δ -π 2-2 π n, n -1, 2, 3, . . . and
Ex0≠E0y, the electric field rotates counterclockwise and
its tip again traces out an ellipse; this is a state of left elliptical
polarization.

[0049] In the general case

Ex=E0x cos(ωt-kz)

Ey=E0y cos(ωt-kz+δ)

where the magnitudes of electric field components E0x and E0y
are not necessarily equal and value of the phase difference δ is
arbitrary, one can derive the curve traced out by the tip of electric
field vector in the xy-plane (which is the plane of electric field
components). By eliminating the phase (ωt kz) we obtain

which specifies a tilted ellipse in Ex and Ey coordinates. The
azimuth angle ψ (0≦ψ≦π 2) between the x-axis and
the major semi-axis of this ellipse then becomes

tan 2 ψ = ( 2 E 0 x E 0 y E 0 x
2 - E 0 y 2 ) cos δ ##EQU00004##

The following relations are also valid between the amplitudes of the
electric field components and the lengths a and b of semi-major and
semi-minor axes which specify the ellipticity of the polarization
ellipse:

a2 b2 E0x2 |E0y2 1.

2. a b 2. E0x2 E0y2 sin δ 2.

where the signs specify the sense of electric field rotation.

tan 2 104 tan α cos δ 3.

where tan α-E0x/E0y and 0≦α≦π/2

sin 2 φ--tan α sin δ 4.

with tan γφ=(b/a), where
-(π/4)≦φ≦)π/4). For the phase difference
δ=0 and δ=π, the ellipse degenerates to

which is the equation of a straight line, and it specifies a linear
polarization. For δ=:π/2 and E0x -E0y=E0, the
elliptical polarization curve reduces to a circle, which defines a
circular polarization

Ex2+Ey2=E02

[0050] The novel methods disclosed herein utilize amplitude modulation of
at least two synchronized polarized Radio Frequency (RF) carrier signals
with an appropriate relationship between their amplitude modulation of
their electric field components and their polarization states to provide
a scanning polarized RF reference source with the desired scanning range,
pattern and frequency. The polarized RF carrier signals are preferably in
GHz range to yield relatively small scanning polarized RF reference
sources.

[0051] As it is noted above, at least two synchronized polarized Radio
Frequency (RF) carrier signals with appropriate relationship between
their amplitude modulation are required to construct the disclosed
polarized RF reference sources with scanning capability. In the following
formulations and for the sake of making the formulations simple, the
present novel method of providing scanning polarized RF reference sources
is described for two synchronized polarized Radio Frequency (RF) carrier
signals E1 and E2, where both are linearly polarized, one with
only a component in the x and one with only a component in the y
direction of the aforementioned Cartesian coordinate system XYZ, as

E1=Ex cos(ω-kz)i

E2=Ey cos(ω-kz |δ)j

where ω is the angular frequency, δ denotes the phase angle
difference between the two electric fields, x and y components of
electric field, k is the z-component of wave number vector. It is
sufficient to concentrate on the behavior of this field in the z-0 plane
to sec the effects of amplitude modulation. Formally amplitude modulation
is represented by replacing the amplitudes Ex and Ey of the
above electric fields by functions of time as

Ex=Ax(t)cos(ωt)

Ey=Ay(t)cos(ωt+δ)

where the modulation amplitudes Ax and Ay may be any functions,
but preferably a superposition of many harmonic functions corresponding
to a range of modulation frequencies and they can represent various
waveforms. In general, the variations of modulation amplitudes are
desired to be significantly slower relative to the fast oscillations of
the carrier waves. i.e., they are almost `constant` on a time duration of
the order of one period of these fast oscillations.

[0052] A relatively simple amplitude modulation of the above polarized
carrier waves may be selected as

Ex=E0x(1+mx sin Ωt)cos ωt

Ey=E0y(1+my sin Ωi)cos(ωtδ)

where Ω is the angular modulation frequency (in our case, the
scanning frequency of the desired scanning polarized RF reference
source), which is much smaller than ω and the constants mx and
my denote the modulation indices of x and y components. These
indices are generally smaller than unity to avoid `over-modulation`.
Specifically we may, for example, choose a left elliptical polarization
(counterclockwise rotation) by setting δ=-π/2 and write

Ex=E0x(1+mx sin Ωt)cos ωt

Ey=E0y(1+my sin Ωt)sin ωt

These components are not periodic functions of a single common frequency
and the curve defined by the electric field vector is not `closed`;
however a particular value of the modulation frequency Ω can be
chosen to satisfy these conditions. Let us impose the condition that
there is a common period T between the modulation and carrier signals.
The periodicity condition for the x-component

Ex=E0x[1+mx sin Ω(t+T)] cos
ω(t+T)=E0x(1+mx sin Ωt)cos ωt

is satisfied if

Ω = n m ω ##EQU00006##

for some integers n and m. Thus if the ratio of modulation and carrier
frequencies is a rational number then one can choose a single period for
the x-component (same is also true for the y-component). In addition, to
have a periodic (closed) curve traced out by the tip of electric field
vector there must be a common period between the field components. The
components Ex and Ey can also be written as

This represents a `modulated ellipse` whose semi-major and semi-minor
`axes` change their lengths periodically and relatively slowly with a
frequency Ω. If the magnitudes of the electric field components are
equal, say to E0, the circular polarization is modulated to an
elliptical one with periodically changing axial lengths as described by

( E x E 0 M x ) 2 + ( E y E 0 M y ) 2
= 1 ##EQU00009##

[0053] One embodiment is the general case or linear polarization in which
the slope of polarization plane is replaced by a periodic function.

Thus if the modulation indices of the two components of the electric
fields E0x and E0y are equal (i.e., if my mx), then
the slope of polarization line remains the same. This isobviously not of
interest since the polarization line is not varied over a certain range.
i.e., the resulting polarized RF reference source does not have a
scanning feature.

[0054] However, if for example, only the y-component is modulated. i.e.,
if mx=0, and an in-phase polarization is considered, the slope of
polarization line is replaced by a simple periodically changing function
given in equation (2), and the polarization line would vary over a
certain range depending on the values of the parameters my,
E0x, and E0y, and the resulting polarized RF reference would
therefore become a scanning polarized RF reference source:

[0055] The equation (1) represents one of the simplest (harmonic) classes
of amplitude modulation for the present novel scanning polarized RF
reference sources constructed with two synchronized polarized Radio
Frequency (RF) carrier signals with appropriate relationship between
their amplitude modulation. It will however, be appreciated by those of
ordinary skill in the art that an infinite number of such classes of
periodic and even non-periodic functions may be formed with two or more
synchronized polarized Radio Frequency (RF) carrier signals with
appropriate relationship between their amplitude modulation to obtain
varieties of preferably periodic and even non-periodic scanning ranges,
rates and "scanning pattern" (hereinafter, the time history of the
polarization line is referred to as the "scanning pattern").

[0056] In addition, even though the above two superimposed linearly
polarized plane waves were in orthogonal directions, the only requirement
to achieve the desired scanning range and pattern is that the two (or
more) waves not be collinear. In fact, for relatively small scanning
ranges, the E vector of the two linearly polarized plane waves may be
desired to be less than 90 degrees apart to minimize the required scanner
power for the same power levels at the receiving sensor position.

[0057] It is noted that the selection of an appropriate scanning pattern
is dependent on the application at hand, for example for the polarized RF
angular orientation measurement sensors previously described, and the
algorithms used to extract the desired information, for example peak
detection and/or pattern matching for angular orientation measurement.

[0058] In one embodiment, the classes of amplitude modulation represented
by equation is used to construct scanning polarized RF reference sources
with two synchronized polarized Radio Frequency (RF) carrier signals as
previously described. One of the simplest versions of this class of
amplitude modulation may be obtained by setting the component mx 0,
thereby obtaining a "scanning pattern" that consists of a simple harmonic
motion, equation (2). For the simple harmonic scanning pattern given by
equation (2), the parameters consisting of the constant magnitudes of the
two components of the electric fields E0x and E0y and the
constant modulation index of the y component my determine the mean
direction of the polarization line and the range of the scanning angle.

[0059] For example, consider the case of mx=0, my=0.5, and
E0x-E0y, and considering that the reference sources are
positioned at the origin of the Cartesian XY coordinate system O, FIG. 3.
Then the polarization line 10 is readily shown to scan from the angle
β1=26.6 deg. (obtained by setting Sin Ω t=-1 in equation
(2) to obtain the slope of the polarization line. i.e.,
β1=tan-1(Ey/Ex)=tan-1(0.5)=26.6 deg.), also
indicated as numeral 12 in FIG. 3, to β2=56.3 deg. (obtained by
setting Sin Ω t=1 in equation (2) to obtain the slope of the
polarization line, i.e.,
β2=tan-1(Ey/Ex)-tan-1(1.5)=56.3 deg.), also
indicated as numeral 13 in FIG. 3, for a total range of the scanning
angle of about γ=29.7 degrees, also indicated as numeral 11 in FIG.
3.

[0060] As can be seen in FIG. 3, with the selected parameters for the
scanning pattern described by equation (2), a range of about 29.7 degrees
11 can be scanned. In a similar manner, by choosing different values for
the constant parameters mx, my, E0x, and E0y,
different mean direction and scanning ranges are obtained with the
scanning pattern described by the equation (1).

[0061] In general, any desired scanning pattern may be implemented with
the proposed method. For example, one may choose scanning patterns with
peaks that are sharper than a simple harmonic sine wave, thereby
increasing the accuracy of a peak detection algorithm. Alternatively, one
may add specially designed patterns that will simplify a pattern
detection algorithm being used and/or to reject noise, and/or to reduce
their susceptibility to detection and jamming, or for other application
specific purposes.

[0062] It is noted that the following method may also be used to provide
two or even more simultaneous and arbitrarily oriented scanning reference
sources. Such multi-range scanning is useful for the establishment of a
network of reference sources and/or to limit the range or radiation when
multiple sensors (for example, munitions and/or weapon platforms) are
using the reference source.

[0063] It is noted that the linearly polarized and synchronized Radio
Frequency (RF) carrier signals used to construct the disclosed scanning
polarized RF reference sources (for example, the two linearly polarized
plane waves Ey and Ex of equation (2) that were superimposed in
the above formulations) may be generated using almost any of the methods
and devices that arc commonly used in the art, including by using
aperture antennas. It is also noted that in many applications, such as in
the guidance and control of most mobile platforms, the angular
orientation and/or position information may not need to be known as a
continuous function of time and information may be required (for example
for guidance and control purposes) only at discrete and sometimes even at
infrequent points of time. In such applications, the scanning polarized
RF reference source needs to provide its signal only when the
aforementioned angular orientation and/or position information is needed
onboard the mobile platform.

[0064] In another embodiment, at least two scanning polarized RF reference
sources may be used so that the aforementioned polarized RF based angular
orientation sensors, for example mounted on a mobile platform, could
determine the position and/or orientation of the sensors, i.e., the
mobile platform, relative to the scanning polarized RF reference sources.

[0065] Now consider the situation in which a scanning polarized RF
reference source 20 is positioned at the origin O of the Cartesian XYZ
coordinate system as shown in FIG. 4. The scanning polarized RF reference
source 20 is considered to have a scanning range 21, with the mean
direction of the polarization line (for example, with a simple harmonic
pattern previously described) indicated by the vector 22. Now let an
object (e.g., a mobile platform) 23 with an embedded aforementioned
polarized RF angular orientation sensor 24 that is properly designed to
receive the carrier frequency signal to be positioned as shown in FIG. 4.
Using well known peak detection techniques, the direction 26 of a line
passing, through the polarized RF angular orientation sensor 24 and
parallel with the direction of the mean direction of the polarization
line, i.e., the vector 22 is determined.

[0066] It is noted that if the line 26 coincides with the mean direction
of the polarization line 22, then the signal received at the polarized RF
angular orientation sensor 24 is maximum and the distance 25 between the
lines 26 and 22 is zero. For example, if the scanning pattern of the
scanning polarized RF reference source 20 is a simple harmonic pattern as
previously described, then the peak of the received signal is reached
when the mean direction of the polarization line 22 intersects the
polarized RF angular orientation sensor 24 and signal received by the
sensor 24 is also substantially a simple harmonic signal (neglecting any
noise and other commonly present sources of distortion). However, if the
distance 25 between the lines 26 and 22 is not zero, then the signal
received by the sensor 24 is distorted with the peak leaning to one side
or the other depending on whether the line 26 is placed below the mean
direction of the polarization line 22 (as shown in FIG. 4) or on its
opposite side.

[0067] The amount of above peak distortion would therefore serve as a
sensory information indicating the direction that the mobile platform 23
has to travel (perpendicular to the line 26) in order to reduce the
distance 25, and would also provide the information onboard the mobile
platform 23 indicating when it is positioned along the mean direction of
the polarization line 22. It can therefore be said that the polarized RF
angular orientation sensor 24 that is attached to the mobile platform 23
can use the signal from the scanning polarized RF reference source 20 to
"home-in" and align itself to the mean direction of the polarization line
22.

[0068] It is noted that if the distance between the scanning polarized RF
reference source 20 and the line 26 is known, then for an arbitrary
positioning of the mobile platform 23, the distance 25 between the lines
22 and 26 can in general be determined from the magnitude of the received
signal.

[0069] Now consider the situation in which two (or more) scanning
polarized RF reference sources 30 and 31 with corresponding mean
directions of the polarization lines 32 and 33, respectively, are used as
shown in FIG. 5. Let also a mobile platform 34 with at least one
polarized RF angular orientation sensor 35 be positioned somewhere a
distance away but in the scanning range of the two scanning polarized RF
reference sources 30 and 31 as shown in FIG. 5. Using the method
described above, the pattern of the signal received at the polarized RF
angular orientation sensor 35 from each one of the two scanning polarized
RF reference sources 30 and 31, the polarized RF angular orientation
sensor 35 would provide sensory information to the mobile platform 34 for
guidance (homing-in) towards the mean direction of the polarization lines
32 and 33, i.e., towards the point of their intersection 36. The only
requirement for this mode of operation of the scanning polarized RF
reference sources is that the two mean directions of the polarization
lines 32 and 33 are not parallel.

[0070] It is noted that the polarization lines 32 and 33 are in fact the
intersections of planes of polarization with the XY plane (FIG. 4). The
aforementioned point of intersection 36 (FIG. 5) is also a line
perpendicular to the above XY plane and directed parallel to the Z axis
of the Cartesian XYZ coordinate system (FIG. 4).

[0071] It is noted that by varying the direction of the polarization line
32 and 33 (FIG. 5), the point of their intersection 36 towards which the
mobile platform 34 is guided can be changed in a dynamic mode.

[0072] It is also noted that by using at least three scanning polarized RF
reference sources that are properly oriented, a mobile platform may be
directed to any position in space.

[0073] In general, by using more scanning polarized RF reference sources
than are necessary, the positioning precision of the above methods is
increased.

[0074] Although the scanning source has been described in terms of RF
energy, other types of energy can also be used, such as x-rays.

[0075] While there has been shown and described what is considered to be
preferred embodiments of the invention, it will, of course, be understood
that various modifications and changes in form or detail could readily be
made without departing from the spirit of the invention. It is therefore
intended that the invention be not limited to the exact forms described
and illustrated, but should be constructed to cover all modifications
that may fall within the scope of the appended claims.